An Introduction to Navier'Stokes Equation and Oceanography

• Κύριος συγγραφέας: Tartar, Luc (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Lecture Notes of the Unione Matematica Italiana, 1
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Continuum physics.; Analysis.; Partial Differential Equations.; Classical Continuum Physics.

 The Introduction to Navier-Stokes Equation and Oceanography corresponds to a graduate course in mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to the lecture notes distributed to the students, as well as short biographical information for all scientists mentioned in the text, the purpose being to show that the creation of scientific knowledge is an international enterprise, and who contributed to it, from where, and when. The goal of the course is to teach a critical point of view concerning the partial differential equations of continuum mechanics, and to show the need for developing new adapted mathematical tools. 

 Basic physical laws and units -- Radiation balance of atmosphere -- Conservations in ocean and atmosphere -- Sobolev spaces I -- Particles and continuum mechanics -- Conservation of mass and momentum -- Conservation of energy -- One-dimensional wave equation -- Nonlinear effects, shocks -- Sobolev spaces II -- Linearized elasticity -- Ellipticity conditions -- Sobolev spaces III -- Sobolev spaces IV -- Sobolev spaces V -- Sobolev embedding theorem -- Fixed point theorems -- Brouwer's topological degree -- Time-dependent solutions I -- Time-dependent solutions II -- Time-dependent solutions III -- Uniqueness in 2 dimensions -- Traces -- Using compactness -- Existence of smooth solutions -- Semilinear models -- Size of singular sets -- Local estimates, compensated integrability -- Coriolis force -- Equation for the vorticity -- Boundary conditions in linearized elasticity -- Turbulence, homogenization -- G-convergence and H-convergence -- One-dimensional homogenization, Young measures -- Nonlocal effects I -- Nonlocal effects II -- A model problem -- Compensated compactness I -- Compensated compactness II -- Differential forms -- The compensated compactness method -- H-measures and variants -- Biographical Information -- Abbreviations and Mathematical Notation.